Fernandez , Marisa and Muñoz, Vicente (2008) An 8-dimensional nonformal, simply connected, symplectic manifold. Annals of Mathematics, 167 (3). pp. 1045-1054. ISSN 0003-486X
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We answer in the affirmative the question posed by Babenko, and Taimanov  on the existence of nonformal, simply connected, compact symplectic manifolds of dimension 8.
|Uncontrolled Keywords:||Nonformal symplectic manifold; Desingularisation process|
|Subjects:||Sciences > Mathematics > Topology|
Sciences > Mathematics > Geometry
I. K. Babenko and I. A. Taimanov, On the formality problem for symplectic manifolds,Contemp. Math. 288 (2001), 1–9.
On existence of nonformal simply connected symplectic manifolds, Russ. Math.Surv. 53 (1998), 1082–1083.
On nonformal simply connected symplectic manifolds, Siberian Math. J. 41 (2000), 204–217.
W. Barth, C. Peters, and A. Van de Ven, Compact Complex Surfaces, Springer-Verlag,New York, 1984.
G. Bredon, Introduction to Compact Transformation Groups, G. R. Cavalcanti, Formality of k-connected spaces in 4k + 3 and 4k + 4 dimensions, Math. Proc. Cambridge Philos. Soc.141 (2006), 101–112.
The Lefschetz property, formality and blowing up in symplectic geometry,Trans. Amer. Math. Soc. 359 (2007), 333–P. Deligne, P. Griffiths, J. Morgan, and D. Sullivan, Real homotopy theory of Kahler manifolds, Invent. Math. 29 (1975), 245–274.
A. Dranishnikov and Y. Rudyak, Examples of nonformal closed (k −1)-connected manifolds of dimensions 4k − 1 and more, Proc. Amer. Math. Soc. 133 (2005), 1557–1561.
M. Fernandez and V. Mu˜noz, On nonformal simply connected manifolds, Topol. Appl.135 (2004), 111–117.
Formality of Donaldson submanifolds, Math. Zeit. 250 (2005), 149–175.
Non-formal compact manifolds with small Betti numbers, Proc. Conf. Contemporary Geometry and Related Topics (Belgrade 2005), Public. Faculty of Math.,University of Belgrade (2006), 231–246.
D. Guan, Examples of compact holomorphic symplectic manifolds which are not Kahlerian II, Invent. Math. 121 (1995), 135–145.
R. Ibañez, Y. Rudyak, A. Tralle, and L. Ugarte, On certain geometric and homotopy properties of closed symplectic manifolds, Topol. Appl. 127 (2002), 33–45.
G. Lupton and J. Oprea, Symplectic manifolds and formality, J. Pure Appl. Algebra 91 (1994), 193–207.
D. McDuff, Examples of symplectic simply connected manifolds with no Kahler structure,J. Differential Geom. 20 (1984), 267–277.
D. McDuff and D. Salamon, Introduction to Symplectic Geometry, second edition, Oxford Math. Monographs,Clarendon Press, Oxford, 1998.
J. Neisendorfer and T. J. Miller, Formal and coformal spaces. Illinois J. Math. 22 (1978), 565–580.
K. Nomizu, On the cohomology of compact homogeneous spaces of nilpotent Lie groups,Ann. of Math. 59 (1954), 531–538.
J. Oprea, The Samelson space of a fibration, Mich. Math. J. 34 (1987), 127–141.
Y. Rudyak and A. Tralle, On Thom spaces, Massey products and nonformal symplectic manifolds, Internat. Math. Res. Notices 10 (2000), 495–513.
A. Tralle and J. Oprea, Symplectic manifolds with no Kahler structure, Lecture Notes in Math. 1661, Springer-Verlag, New York, 1997.
|Deposited On:||20 Nov 2012 12:42|
|Last Modified:||07 Feb 2014 09:42|
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